Rapid progress in the modeling of biological structures and simulation of their development has occurred over the last few years. It has been coupled with the visualization of simulation results, which has lead to a better understanding of morphogenesis and given rise to new procedural techniques for realistic image synthesis. This paper characterizes selected models of morphogenesis with a significant visual component. KEYWORDS: developmental models in biology, morphogenesis, simulation and visualization of biological phenomena, realistic image synthesis, reaction-diffusion, diffusionlimited growth, cellular automaton, L-system. How far mathematics will suffice to describe, and physics to explain, the fabric of the body, no man can forsee. D'Arcy Thompson, On Growth and Form [40]

Evolution of Lindenmayer Systems (L-Systems) provides a powerful method for creating complex computer graphics and animations. This paper describes an interactive modelling system for computer graphics in which the user is able to "evolve" grammatical rules and surface equations. Starting from any initial L-System grammar the evolution proceeds via repeated random mutation and user selection. Sub-classes of the mutation process depend on the context of the current symbol or rule being mutated and include mutation of: parametric equations and expressions, growth functions, rules and productions. As the grammar allows importation of parametric surfaces, these surfaces can be mutated and selected as well. The mutated rules are then interpreted to create a three-dimensional, time-dependent model composed of parametric and polygonal geometry. L-System evolution allows with minimal knowledge of L-Systems to create complex, "lifelike " images and animations that would be difficult and far more time-consuming to achieve by writing rules and equations explicitly.

We introduce the Clonal Mosaic (CM) model for the synthesis of mammalian coat patterns, present its implementation for modeling and display purposes, and give a few examples of generated patterns. The model is based on cell division and cell-to-cell interactions, and it can generate repeating spotted and striped patterns occurring in several species of mammals, especially the big cats and giraffes. From a

: Volumetric textures are able to represent complex repetitive data such as foliage, fur and forests by storing one sample of geometry in a volumetric texel to be mapped onto a surface. This volume consists in samples of densities and reflectances stored in voxels. The texel can be prefiltered similarly to the mip-mapping algorithm, giving an efficient rendering in ray-tracing with low aliasing, using a single ray per pixel. Our general purpose is to extend the volumetric texture method in order to provide a convenient and efficient tool for modeling, animating and rendering highly complex scenes in ray-tracing. We illustrate our method with verdant landscapes such as forests and lawns. In our previous work, we have dealt with the multiscale volume representation and texel animation. In this paper, we show how to convert usual 3D models into texels, and how to render texels mapped onto any mesh type. Solving these two issues makes the method usable for a designer. Key-words: volumet...

In these notes we survey applications of L-systems to the modeling of plants, with an emphasis on the results obtained since the comprehensive presentation of this area in The Algorithmic Beauty of Plants [61]. The new developments include: ffl a better understanding of theoretical issues pertinent to graphical applications of L-systems, ffl extensions to programming techniques based on L-systems, and ffl an extension of the range of phenomena expressible using L-systems. Keywords: L-system, fractal, plant, modeling, simulation, realistic image synthesis, emergence, artificial life. 1 Introduction In 1968, Aristid Lindenmayer introduced a formalism for simulating the development of multicellular organisms, subsequently named L-systems [36]. This formalism was closely related to abstract automata and formal languages, and attracted the immediate interest of theoretical computer scientists [67]. The vigorous development of the mathematical theory of L-systems [70, 27, 66] was follow...

In this paper, we explore the problem of interactively manipulating plant models without sacrificing their botanical accuracy. The primary technical contribution of the paper is a method for interactively manipulating plant structures using a inverse-kinematics optimization technique. The branches of the plant are endowed with flexural and torsional stiffnesses, and these are used in the IK optimization. We demonstrate our approach with several examples of plant models arranged in this fashion. Keywords: botanical modeling, L-system, plant arrangement, inverse-kinematics, optimization, interactive techniques 1 Introduction Lindenmayer-systems, or L-systems for short, were introduced as a theoretical model of plant development [5]. In the hands of computer graphics researchers, L-systems have evolved into a powerful tool for creating biologically faithful and visually realistic models of plants, capable of simulating their growth and interaction with the environment [7, 10, 11]. The...

We consider classes of sets of r-adic expansions of reals specified by means of the theory of formal languages or automata theory. It is shown how these specifications are used to calculate the Hausdorff dimension and Hausdorff measure of such sets. Since the appearence of Mandelbrot's 11 book "Fractals, Form, Chance and Dimension " Fractal Geometry as a means providing a theory describing many of the seemingly complex patterns in nature and the sciences has become popular not only in the sciences (cf. Peitgen and Saupe 13 ), but also in computer science. Here Barnsley's 3 "Computational Fractal Geometry" aims at a practical description of fractal patterns by so-called Iterative Function Systems (IFS). Besides IFS several other computational methods for the description (generation) of fractal images involving concepts of Automata or Formal Language Theory have been developed (see e.g. Berstel and Morcrette 4 , Berstel and Nait-Abdallah 5 , Culik and Dube 6; 7 , Prusinki...

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L-Systems have traditionally been used as a popular method for the modelling of spacefilling curves, biological systems and morphogenesis. In this paper, we adapt string rewriting grammars based on L-Systems into a system for music composition.

This paper presents a method to simulate growth phenomena, and its application to the modeling of complex organic shapes (e.g., plants organs) and folded surfaces. Our main contribution is the interactive and stable resolution of the mechanical problem of growth-induced deformations, based on the minimization of the energy due to the various constraints in the shell. From this, we propose a new modeling approach based on a set of growing tools: The user can apply ’hot spots’, ’hot curves’, or paint growing parameters on the surface to grow. Growth can be simulated either simultaneously to the user interaction, or once all parameters have been settled on the surface (which allows the use of textures of parameters and procedural operations). The main parameters are the intensity and anisotropy of growth, as well as their variations over time. Geometric constraints and plasticity can also be considered. As our results show shapes can fold, bend, and curl as in nature, which deforming tools such as displacement map could not achieve. We demonstrate our tool with an interactive session and a gallery of shapes easily produced. 1. Introduction and Previous